Answer:
The nth term of the given sequence
Step-by-step explanation:
<u><em>Explanation:-</em></u>
Given sequence -5,-4,-1,4,11,20,31
a₀ = -5
a₁ = a₀ +1 = -5 +1 = -4
a₂ = a₁ + 3 = -4+3 = -1
a₃ = a₂ + 5 = -1 +5 = 4
a₄ = a₃ + 7 = 4 + 7 =11
a₅ = a₄ + 9 = 11+9 = 20
a₆ = a₅ + 11 = 20+11 = 31
a₇ = a₆ + 13 = 31 +13 =44
and so on
The nth term of the given sequence
Answer:
a = 3
b = 2
c = 0
d = -4
Step-by-step explanation:
Form 4 equations and solve simultaneously
28 = a(2)³ + b(2)² + c(2) + d
28 = 8a + 4b + 2c + d (1)
-5 = -a + b - c + d (2)
220 = 64a + 16b + 4c + d (3)
-20 = -8a + 4b - 2c + d (4)
(1) + (4)
28 = 8a + 4b + 2c + d
-20 = -8a + 4b - 2c + d
8 = 8b + 2d
d = 4 - 4b
Equation (2)
c = -a + b + d + 5
c = -a + b + 4 - 4b+ 5
c = -a - 3b + 9
28 = 8a + 4b + 2c + d (1)
28 = 8a + 4b + 2(-a - 3b + 9) + 4 - 4b
28 = 6a - 6b + 22
6a - 6b = 6
a - b = 1
a = b + 1
220 = 64a + 16b + 4c + d (3)
220 = 64(b + 1) + 16b + 4(-b - 1 - 3b + 9) + 4 - 4b
220 = 60b + 100
60b = 120
b = 2
a = 2 + 1
a = 3
c = -3 - 3(2) + 9
c = 0
d = 4 - 4(2)
d = -4
Hi!
So really focus on the fact that he started at $230, and then added an amount of money which we'll call x, which made his total equal $599.
Take the parts I put in bold, and write the equation.
$230 + x = $599
Now we need to find x.
Whatever we do to the equation, we do it to both sides.
Our goal is to isolate x on one side.
Subtract 230 from both sides.
$230 - $230 + x = $599 - $230
x = $369
The answer is A. $230 + x = $599 x = $369
Hope this helps! :)
-Peredhel
Answer:
the probability that the x-coordinate of the point is negative and the y-coordinate of the point is positive is 16.36%
Step-by-step explanation:
Assuming that each point has the same probability to be chosen ( uniform probability distribution in the rectangle area ) then the probability of choosing a negative x-coordinate and positive y-coordinate is the ratio of the area with those requirements over the total area of the rectangle.
therefore
Ar= area of negative x-values and positive y-values = (-3)*6 = 18
AT= total area of the rectangle = [8-(-3) ]*[6-(-4)] = 110
then
probability = Ar/AT = 18/110 = 0.1636 = 16.36%
